Graphics Gems V (IBM Version)

IV.3

Circular Arc Subdivision

Turkowski Ken,     Apple Computer, Inc. Cupertino, California. E-mail address: [e-mail]

Introduction

This gem presents an algebraic solution to the rendering problem of circular arcs. These forms commonly arise in graphic design. For instance, well-designed typefaces may apply a very slight curvature on a portion of a letterform to produce a profound aesthetic effect. ¹

A circular arc may be represented in terms of the center and radius of its parent circle, plus the starting and ending angles θ_st and θ_end. This suggests a first-principles solution that generates successive points on the arc by evaluating the sine and cosine of a series of intermediate angles:

Clearly, this approach is computationally ...